Tomographic 3D reconstruction through linear inversion for breast microwave imaging

In the present thesis we address the problem of detecting and localizing a small spherical target with characteristic electrical properties inside a volume of cylindrical shape, representing female breast, with MWI. One of the main works of this project is to properly extend the existing linear inversion algorithm from planar slice to volume reconstruction; results obtained, under the same conditions and experimental setup are reported for the two different approaches. Preliminar comparison and performance analysis of the reconstruction algorithms is performed via numerical simulations in a software-created environment: a single dipole antenna is used for illuminating the virtual breast phantom from different positions and, for each position, the corresponding scattered field value is registered. Collected data are then exploited in order to reconstruct the investigation domain, along with the scatterer position, in the form of image called pseudospectrum. During this process the tumor is modeled as a dielectric sphere of small radius and, for electromagnetic scattering purposes, it's treated as a point-like source. To improve the performance of reconstruction technique, we repeat the acquisition for a number of frequencies in a given range: the different pseudospectra, reconstructed from single frequency data, are incoherently combined with MUltiple SIgnal Classification (MUSIC) method which returns an overall enhanced image. We exploit multi-frequency approach to test the performance of 3D linear inversion reconstruction algorithm while varying the source position inside the phantom and the height of antenna plane. Analysis results and reconstructed images are then reported. Finally, we perform 3D reconstruction from experimental data gathered with the acquisition system in the microwave laboratory at DIFA, University of Bologna for a recently developed breast-phantom prototype; obtained pseudospectrum and performance analysis for the real model are reported.

Teos-based consolidants for stone conservation: evaluation of the effects and testing by x-ray imaging

Natural stones have been widely used in the construction field since antiquity. Building materials undergo decay processes due to mechanical,chemical, physical and biological causes that can act together. Therefore an interdisciplinary approach is required in order to understand the interaction between the stone and the surrounding environment. Utilization of buildings, inadequate restoration activities and in general anthropogenic weathering factors may contribute to this degradation process. For this reasons, in the last few decades new technologies and techniques have been developed and introduced in the restoration field. Consolidants are largely used in restoration and conservation of cultural heritage in order to improve the internal cohesion and to reduce the weathering rate of building materials. It is important to define the penetration depth of a consolidant for determining its efficacy. Impregnation mainly depends on the microstructure of the stone (i.e. porosity) and on the properties of the product itself. Throughout this study, tetraethoxysilane (TEOS) applied on globigerina limestone samples has been chosen as object of investigation. After hydrolysis and condensation, TEOS deposits silica gel inside the pores, improving the cohesion of the grains. X-ray computed tomography has been used to characterize the internal structure of the limestone samples,treated and untreated with a TEOS-based consolidant. The aim of this work is to investigate the penetration depth and the distribution of the TEOS inside the porosity, using both traditional approaches and advanced X-ray tomographic techniques, the latter allowing the internal visualization in three dimensions of the materials. Fluid transport properties and porosity have been studied both at macroscopic scale, by means of capillary uptake tests and radiography, and at microscopic scale,investigated with X-ray Tomographic Microscopy (XTM). This allows identifying changes in the porosity, by comparison of the images before and after the treatment, and locating the consolidant inside the stone. Tests were initially run at University of Bologna, where characterization of the stone was carried out. Then the research continued in Switzerland: X-ray tomography and radiography were performed at Empa, Swiss Federal Laboratories for Materials Science and Technology, while XTM measurements with synchrotron radiation were run at Paul Scherrer Institute in Villigen.

Compressed sensing in digital tomosynthesis reconstruction

In this work we study a model for the breast image reconstruction in Digital Tomosynthesis, that is a non-invasive and non-destructive method for the three-dimensional visualization of the inner structures of an object, in which the data acquisition includes measuring a limited number of low-dose two-dimensional projections of an object by moving a detector and an X-ray tube around the object within a limited angular range. The problem of reconstructing 3D images from the projections provided in the Digital Tomosynthesis is an ill-posed inverse problem, that leads to a minimization problem with an object function that contains a data fitting term and a regularization term. The contribution of this thesis is to use the techniques of the compressed sensing, in particular replacing the standard least squares problem of data fitting with the problem of minimizing the 1-norm of the residuals, and using as regularization term the Total Variation (TV). We tested two different algorithms: a new alternating minimization algorithm (ADM), and a version of the more standard scaled projected gradient algorithm (SGP) that involves the 1-norm. We perform some experiments and analyse the performance of the two methods comparing relative errors, iterations number, times and the qualities of the reconstructed images. In conclusion we noticed that the use of the 1-norm and the Total Variation are valid tools in the formulation of the minimization problem for the image reconstruction resulting from Digital Tomosynthesis and the new algorithm ADM has reached a relative error comparable to a version of the classic algorithm SGP and proved best in speed and in the early appearance of the structures representing the masses.

Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.